| This paper is concerned with fixed point theorems and their applications and algorithm of variational inequalities. In chapter one, acyclic mappings is discussed. Some new fixed point theorems for a family of set-valued mappings in product space of topological vector spaces are obtained. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems are established. Chapter two, some new collectively fixed point theorems and existence theorems of maximal element involving better admissible mappings in G ?convex spaces are proved. As applications some equilibrium existence theorems of abstract economies are obtained. In chapter three, a class of mixed variational inequalities is studied. By using the ε?enlargements of maximal monotone operators, we get a splitting inertial proximal algorithm. Moreover, we also prove the weak convergence criteria. |
